The field of digital data compression and in particular digital image compression has attracted great interest for some time.
In the field of digital image compression, many different techniques have been utilised. In particular, one popular technique is the JPEG standard which utilises the discrete cosine transform (DCT) to transform standard size blocks of an image into corresponding cosine components. In this respect, the higher frequency cosine components are heavily quantised so as to assist in obtaining substantial compression factors. The heavy quantisation is an example of a "lossy" technique of image compression. The JPEG standard also provides for the subsequent lossless compression of the transformed coefficients.
Recently, the field of wavelet transforms has gained great attention as an alternative form of data compression. The wavelet transform has been found to be highly suitable in representing data having discontinuities such as sharp edges. Such discontinuities are often present in image data or the like.
Although the preferred embodiments of the present invention will be described with reference to the compression of image data, it will be readily evident that the preferred embodiment is not limited thereto. For examples of the many different applications of Wavelet analysis to signals, reference is made to a survey article entitled "Wavelet Analysis" by Bruce et. al. appearing in IEEE Spectrum, October 1996 page 26-35. For a discussion of the different applications of wavelets in computer graphics, reference is made to "Wavelets for Computer Graphics", I. Stollinitz et. al. published 1996 by Morgan Kaufmann Publishers, Inc.
A number of image coding techniques are known which utilise a linear transformation of the input image to reduce both inter-pixel correlation and coefficient coding overhead. These techniques include the JPEG image compression standard and the federal bureau of investigation (FBI) fingerprint image compression standard. As noted previously, the JPEG standard utilises a discrete cosine transform (DCT) of the image data, while the FBI standard uses a discrete wavelet transform (DWT).
Previous techniques for encoding the coefficients of a DWT include the embedded zerotree wavelet (EZW) method (U.S. Pat. Nos. 5,412,741, 5,315,670, 5,321,776) and set partitioning in hierarchical trees (SPIHT). These techniques first apply a conventional DWT to the source image data to produce the small low frequency representation of the image (called the LL subband) and a number of high frequency, or detail, subbands (called HL, LH and HH subbands). The techniques then utilise the correlation between different frequency subbands, at the same orientation, to predict zero coefficients down the wavelet tree. These methods have been developed for natural images that are assumed to have a 1/f frequency spectrum. They use a conventional DWT decomposition that continually decomposes the low frequency image subbands. Therefore, they often do not efficiently handle images, such as fingerprint images, that do not conform to the 1/f model.
The FBI image compression standard was specifically designed to compress fingerprint images and so uses a non-conventional DWT, decomposing subbands other than the LL subband. However, the subbands decomposed are predefined and can not adapt to either fingerprints with different statistics or to new image types.